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Teaching Square Numbers

Beautiful gemstones make math more enjoyable!

Square numbers are, well, square!
I have begun working with a slightly older student (middle school) and we began with square numbers, as it was one of the topics they needed to review.  I am delighted to know of these methods, and to be able to share them with others.  I really see math come alive, and the student become so much more engaged than with mere drill.

I have showed this little example to adults even, who were quite amazed to see that square numbers actually produce physical squares.  So often, in traditional schooling, terminology is used without depth of understanding, often, even by the teachers.  When we begin to use hands on, and even artistic methods, one is able to grasp a concept and create knowledge, which is the only true basis for learning.

We began in the lower left hand corner and put 1 row and 1 column (hence only one gemstone or box).  This is 1 x 1

then we put 2 rows and 2 columns, giving us 2 x 2, or 4.

we continued with 3 rows and 3 columns, giving us 3 x 3, or 9.

and thus we continued adding rows and columns, counting the gems, and making beautiful squares.

This lesson might be taught in 2nd/ 3rd grade, but is excellent for older students who are not strong in math, or who simply have been taught with more traditional methods.  This lesson really seemed to have a little of something for everyone.

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